hua0127 兄的答案是對的
整理一下算式
x = 201,[x] + [2x] + [3x] + [4x] = 2010
x = 202,[x] + [2x] + [3x] + [4x] = 2020
故 201 < x < 202
令 x = 201 + y (0 < y < 1)
[x] + [2x] + [3x] + [4x] = 201 * 10 + [2y] + [3y] + [4y] = 2014
[2y] + [3y] + [4y] = 4
(1) 0 < y < 1/2
[2y] + [3y] + [4y] ≦ 0 + 1 + 1 = 2,不合
(2) 1/2 ≦ y < 2/3
[2y] + [3y] + [4y] = 1 + 1 + 2 = 4,合
(3) 2/3 ≦ y < 1
[2y] + [3y] + [4y] ≧ 1 + 2 + 2 = 5,不合
故 201又(1/2) ≦ x < 201又(2/3)